Evaluating All Six Trigonometric Functions
Finding the values of all six trigonometric functions of an angle given a right triangle
tags:
Cosecant Cosine Cotangent How-To Precalculus Pythagorean Theorem Right Triangle Secant Sine Tangent TrigonometryEvaluating the Other Trigonometric Functions Given Sine
Author: Elena Welch
The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Reveal Answer" to reveal the answer to the problem.
Problem: Given that \(\sin(\theta)=\dfrac{\sqrt{3}}{2}\) and \(\theta\) is an acute angle, find all other trigonometric values for \(\theta.\)
\(\csc \theta =\dfrac{2\sqrt{3}}{3}\)
\(\cos \theta = \dfrac{1}{2}\qquad \sec \theta = 2\)
\(\tan \theta = \sqrt{3} \qquad \cot \theta = \dfrac{\sqrt{3}}{3}\)
\(\cos \theta = \dfrac{1}{2}\qquad \sec \theta = 2\)
\(\tan \theta = \sqrt{3} \qquad \cot \theta = \dfrac{\sqrt{3}}{3}\)
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MLC WIR 20B M151 week8 #6
Using antidifferentiation to find the height of a cliff from the impact speed of a dropped stone
MLC WIR 20B M151 week10 #24e
Using u-substitution to evaluate an indefinite integral
WIR 20B M152 V97
Finding the area of a region defined using polar coordinates
WIR 20B M152 V98
Finding the area of a region defined using polar coordinates
WIR 20B M152 V99
Finding the area of a region defined using polar coordinates
WIR 20B M152 V79
Finding the Maclaurin series of a function
WIR 20B M152 V80
Evaluating a definite integral by rewriting the integrand as its Maclaurin series
WIR 20B M152 V69
Determining if a series is absolutely convergent, conditionally convergent, or divergent.
MATH 152: Integration by Parts Exercise 3
Solving an indefinite integral with cosine using integration by parts
MATH 152: Integration by Parts Exercise 9
Using integration by parts twice for an integral with sine and an exponential function
WIR 20B M152 V24
Evaluating an integral using integration by parts
WIR 20B M152 V25
Evaluating an integral using integration by parts
WIR 20B M152 V26
Evaluating an integral using integration by parts
WIR 20B M152 V27
Evaluating an integral using trigonometric identities
MATH 152: Trigonometric Integrals Exercise 6
Using a trigonometric identity to integrate an even power of cosine
MATH 152: Trigonometric Substitution Exercise 1
Using trigonometric substitution to evaluate an indefinite integral
MATH 152: Trigonometric Substitution Exercise 2
Using trigonometric substitution to evaluate an indefinite integral
MATH 152: Trigonometric Substitution Exercise 3
Using trigonometric substitution to evaluate an indefinite integral
MATH 152: Trigonometric Substitution Exercise 4
Using trigonometric substitution to evaluate an indefinite integral
MATH 152: Trigonometric Substitution Exercise 5
Using trigonometric substitution to evaluate a definite integral
MATH 152: Trigonometric Substitution Exercise 6
Using trigonometric substitution to evaluate a definite integral
MATH 152: Trigonometric Substitution Exercise 7
Using trigonometric substitution to evaluate an indefinite integral
MATH 152: Trigonometric Substitution Exercise 8
Using trigonometric substitution to evaluate an indefinite integral
Dot Product: MATH 171 Problems 7 & 8
Proofs of the Cauchy-Schwarz Inequality and a property of vector projections
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40
Review of derivatives and tangent lines to functions and vector equations
Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19
Mean Value Theorem and using derivatives to find the shape of curves
Review for Common Exam: MATH 151 Exam 3 Review Problems 25-30
Antiderivatives and physics applications
Approximations and Exponentials: MATH 151 2.6 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Limits and Asymptotes: MATH 151 2.6 Problems 7-11
Limits at infinity and asymptotes, along with physics applications
Limits and Asymptotes: MATH 151 2.7 Problems 7-11
Limits at infinity, asymptotes, and tangent lines
Review for the Common Exam: MATH 151 3.1 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Review for the Common Exam: MATH 151 3.1 Exam 1 Review Problems 36-40
Review of derivatives and tangent lines to functions and vector equations
Review for the Common Exam: MATH 151 3.2 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Review for the Common Exam: MATH 151 3.2 Exam 1 Review Problems 36-40
Derivatives and tangents to curves
Approximations and Exponentials: MATH 151 3.4 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Studying the Shape of Curves: MATH 151 4.1 Problems 2-7
Using derivatives to find properties of graphs
Studying the Shape of Curves: MATH 151 Problems 2-7
Using derivatives to find properties of graphs
Riemann Sums: MATH 151 5.1 Problems 1-5
Riemann sums, including approximating areas under curves.
Integration by Substitution: MATH 151 5.5 Problems 13 & 14
Examples of integration by substitution
Integration by Parts: MATH 172 Problems 1 & 2
Proving the formula for integration by parts and a reduction formula
WIR1 20B M251 V15
Calculating the length of the cross product of two vectors given information about the vectors
WIR2 20B M251 V7
Finding the limit of a three-dimensional vector function
WIR2 20B M251 V8
Finding a vector equation for the tangent line to a three-dimensional vector function
WIR3 20B M251 V9
Finding the partial derivatives of a function of two variables
WIR6 20B M251 V4
Converting a double integral to a double integral in polar coordinates
WIR9 20B M251 V6
Finding the curl and divergence of a three dimensional vector field
WIR10 20B M251 V9
Using the Divergence Theorem to evaluate the surface integral of a vector field
WIR 20B M152 V49
Determining if a sequence is increasing, decreasing, or not monotonic and if it is bounded
Special Right Triangles Exercise 1
Special Right Triangles Exercise 1
Special Right Triangles Exercise 2
Special Right Triangles Exercise 2
Trig Identities Exercise 1
Using the reciprocal and ratio trig identities to simplify an expression
Trig Identities Exercise 2
Using the Pythagorean Identities to simplify a trig expression
Deriving the Secondary Pythagorean Trig Identities
Using the Pythagorean Trig Identity to derive the secondary Pythagorean Identities
Trigonometric Proofs Exercise 1
Using the Reciprocal, Ratio, and Pythagorean Identities to verify a trig identity
Trigonometric Proofs Exercise 2
Proving a trigonometric identity involving secant, cotangent, and tangent
Trigonometric Proofs Exercise 3
Proving a trig identity involving sine and cosine
Trigonometric Proofs Exercise 4
Proving a trig identity involving sine, cosine, and cotangent
Solving Trig Equations Using Identities Exercise 7
Solving a trig equation with cotangent and sine using trig identities
Solving Trig Equations Using Identities Exercise 1
Using the Even/Odd and Cofunction Identities to solve an equation with sine
Math 304 Section 2.2 Exercise 2
Finding the values of \(\theta\) that makes a matrix with trig functions invertible
Math 304 Section 3.3 Exercise 9
Determining whether trigonometric functions are linearly independent
Math 304 Section 3.4 Exercise 5
Finding the dimension of the subspace spanned by a set of functions
Equation of a Line Given Two Points
Writing the equation of a line passing through two points
Slope-Intercept Form of an Equation for a Line
Writing the equation of a line through two points in slope-intercept form
Standard Form of an Equation for a Line
Writing the equation of a graphed line in standard form
Factoring a Quadratic
Factoring a quadratic polynomial
Factoring a Quadratic (2)
Factoring a quadratic function
Factoring by Grouping
Factoring a cubic polynomial by grouping
Factoring Out the Greatest Common Factor
Finding the greatest common factor of a polynomial and then factoring it out
Factoring a Quadratic: Leading Coefficient is 1
Factoring a quadratic where the leading coefficient is 1
Factoring a Quadratic: Leading Coefficient is Not 1
Factoring quadratics where the leading coefficient is not 1
Factoring by Grouping (2)
Factoring several polynomials by grouping
Factoring a Difference of Two Squares
Factoring a difference of two squares
Factoring a Sum and Difference of Cubes
Factoring a sum of cubes and a difference of cubes
Simplifying a Rational Expression
Simplifying a rational expression
Subtracting Rational Expressions
Adding and then simplifying two rational expressions
Multiplying Rational Expressions
Multiplying two rational expressions and then simplifying
Dividing Rational Expressions
Dividing rational expressions and then simplifying the answer
Adding Rational Expressions
Adding two rational expressions and then simplifying the answer
Holes and Asymptotes of Rational Functions
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Holes and Asymptotes of Rational Functions (2)
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Matching a Rational Function with its Graph
Matching a rational function with its graph
Roots of a Quadratic
Using the quadratic formula to find the roots of a function
Roots of a Polynomial
Finding the roots of a cubic polynomial
Roots of a Square Root Function
Finding the roots of a square root function
Roots of a Function with an Absolute Value
Finding the roots of a function with an absolute value
Domain of a Rational Function
Finding the domain of a rational function
Domain of a Rational Function (2)
Finding the domain of a rational function
Domain of Function with Roots
Finding the domain of a function with a fraction and radicals
Domain of a Square Root Function
Finding the domain of a function with a quadratic inside a square root
Composition of Polynomial Functions
Finding the composition of two functions
Function Composition with a Rational Function
Finding the composition of a rational function and a quadratic
Composition of Logarithmic and Exponential Functions
Finding the composition of two functions with exponentials and logarithms
Composition of Square Root and Power Functions
Finding the composition of two functions with a square root and a fractional exponent
Composition of Cube Root and Power Functions
Finding the composition of two functions with a cube root and a fractional exponent
Inverse of a Linear Function
Finding the inverse of a linear function and its domain
Inverse of a Square Root Function
Finding the inverse of a square root function and its domain
Inverse of a Rational Function
Finding the inverse of a rational function and its domain
Inverse of a Rational Function (2)
Finding the inverse of a rational function and its domain
Difference Quotient of a Quadratic
Finding and simplifying the difference quotient for a quadratic function
Difference Quotient of a Rational Function
Finding and simplifying the difference quotient for a rational function
Difference Quotient of a Square Root Function
Finding and simplifying the difference quotient for a square root function
Solving an Inequality with a Polynomial
Solving an inequality with a polynomial by factoring and using a sign diagram
Solving an Inequality with a Rational Function
Solving an inequality with a rational expression by factoring and using a sign diagram
Solving an Inequality with a Sum of Rational Functions
Solving an inequality with two rational expressions using a sign diagram
Solving an Inequality with by Finding a Least Common Denominator
Solving an inequality with a rational expression using a sign diagram
Solving an Inequality with a Quadratic Function
Solving an inequality with a quadratic by factoring and using a sign diagram
Absolute Maximum or Minimum of a Quadratic
Finding the absolute maximum or absolute minimum of a quadratic
Standard Form of a Quadratic
Writing the standard form of quadratic function given its vertex and one other point
Component Form and Magnitude of a Vector
Finding the component form and magnitude for a vector between two points
Vector Addition and Subtraction and Scalar Multiplication
Performing calculations with vectors including addition, subtraction, and scalar multiplication
Dot Product
Calculating the dot product for three pairs of vectors
Finding a Unit Vector
Finding a unit vector in the direction of a given vector
Solving a System of Equations
Solving a system of two linear equations using the method of substitution
Solving a System of Equations (2)
Solving a system of two linear equations using the method of substitution
Solving a System of Equations (3)
Solving a system of two linear equations
Solving a System of Nonlinear Equations
Solving a system on two equations where one is linear and one is quadratic
An Equation with an Exponential Function
Solving a equation with an exponential function
An Equation with Exponential Functions of Different Bases
Solving an equation with two exponential functions with different bases
Factoring a Quadratic-Like Equation with Exponentials
Solving an equation with exponential functions by factoring
Factoring an Equation with Exponentials
Solving a equation with exponential functions by factoring
Population Model with Exponential Growth
Finding the size of a population of rabbits with exponential growth
Population Model with Exponential Decay
Finding the size of a population of rabbits with exponential decay
Horizontal Asymptote of an Exponential Function
Finding the horizontal asymptote of an exponential function
Horizontal Asymptote of an Exponential Function (2)
Finding the horizontal asymptote of an exponential function
Horizontal Asymptote of an Exponential Function (3)
Finding the horizontal asymptote of an exponential function
Expanding a Logarithmic Expression
Expanding a logarithmic expression using logarithm properties
Condensing a Logarithmic Expression
Condensing logarithmic expressions into a single logarithm
Evaluating Logarithmic Expressions
Finding the exact value of logarithms using logarithmic properties
Vertical Asymptote of a Logarithmic Function
Finding the vertical asymptote of a logarithmic function
Vertical Asymptote of a Logarithmic Function (2)
Finding the vertical asymptote of a logarithmic function
Domain and x-intercepts of a Logarithmic Function
Finding the domain and x-intercepts of a logarithmic function
Domain and x-intercepts of a Logarithmic Function (2)
Finding the domain and x-intercepts of a logarithmic function
Solving an Equation with Logarithms
Solving a logarithmic equation using properties of logarithms
Solving an Equation with a Logarithmic Function
Solving a logarithmic equation using properties of logarithms
WIR 20B M152 V57
Using the comparison test to determine if a series converges or diverges
WIR 20B M152 V58
Using the comparison test to determine if a series converges or diverges
WIR 20B M152 V59
Using the limit comparison test to determine if a series converges or diverges
WIR 20B M152 V62
Using the Alternating Series Test to determine if a series converges or diverges
WIR 20B M152 V63
Using the Alternating Series Test to determine if a series converges or diverges
WIR 20B M152 V64
Using the Alternating Series Test to determine if a series converges or diverges
Generating and Plotting Sequences in Python
Using Python to numerically, graphically, and analytically find the limit of a sequence
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative